A chain tug on non drive side will do nothing to stop this: its the leverage of the brake pushing the axle backwards not forwards, which is all the chain tug will pull against. (try looseing the qr a smidge and you will see this start to happen if you just rock the bike back and forth).
This is why slotty dropout on-ones have disc mount inside the rear triangle (there is some blurb somewhere on the website about this), some frames have the whole dropouts slide forward and a vertical dropout within this assembly, and some have eccentric bottom brackets and normal dropouts. Was never really an issue before disc brakes hence horizontal dropouts being the norm for old mtb's, and all bmx/track/fixes etc.
Only solution for this arrangment (ie horizontal dropouts and disc tabs on seat stay) is to do rear axle up much tighter. I had a jump/fun bike (commencal maxmax) -it was fine with a nutted axle done up nice and tight and I was always on the brakes on it. 😳